5x-2/(x+3)=0

Solution for 5x-2/(x+3)=0 equation:

5x-2/(x+3)=0


Domain of the equation: (x+3)!=0

We move all terms containing x to the left, all other terms to the right

x!=-3

x∈R


We multiply all the terms by the denominator


5x*(x+3)-2=0

We multiply parentheses

5x^2+15x-2=0

a = 5; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·5·(-2)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{265}}{2*5}=\frac{-15-\sqrt{265}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*5}=\frac{-15+\sqrt{265}}{10}
$